Boundedness of higher order Riesz transforms associated with Schrodinger type operator on generalized Morrey spaces

Bijun Ren, Hui Wang
2017 Journal of Nonlinear Science and its Applications  
Let L 2 = (−∆) 2 + V 2 be a Schrödinger type operator, where V = 0 is a non-negative potential and belongs to the reverse Hölder class RH q for q n/2, n 5. The higher Riesz transform associated with L 2 is denoted by R = ∇ 2 L − 1 2 2 and its dual is denoted by R * = L − 1 2 2 ∇ 2 . In this paper, we investigate the boundedness of higher Riesz transforms and their commutators on the generalized Morrey spaces related to some non-negative potential.
doi:10.22436/jnsa.010.05.42 fatcat:qpeqrr6mbrfd7pzfpp2u5i2pei